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Existence of solutions of impulsive boundary value problems for singular fractional differential systems

Yuji Liu (2017)

Mathematica Bohemica

A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point...

Existence of two solutions for quasilinear periodic differential equations with discontinuities

Nikolaos S. Papageorgiou, Francesca Papalini (2002)

Archivum Mathematicum

In this paper we examine a quasilinear periodic problem driven by the one- dimensional p -Laplacian and with discontinuous forcing term f . By filling in the gaps at the discontinuity points of f we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions,...

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